# An Algebra Problem from RMO

Algebra Level 3

$\begin{cases} f(x)={ x }^{ 3 }+{ a }x^{ 2 }+bx+c \\ g(x)={ x }^{ 3 }+{ b }x^{ 2 }+cx+a \end{cases}$ Given that $$a, b, c$$ are integers with $$c\neq 0$$ and the following conditions hold for the above functions:

(a) $$f(1) = 0$$;

(b) the roots of $$g(x) = 0$$ are the squares of the roots of $$f(x) = 0$$.

Find the absolute value of $({ a }^{ 2013 }+{ b }^{ 2013 }+{ c }^{ 2013 }).$

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